login
A355902
Start with a 2 X n array of squares, join every vertex on top edge to every vertex on bottom edge; a(n) = one-half the number of cells.
2
0, 3, 10, 26, 56, 112, 196, 331, 522, 790, 1138, 1615, 2204, 2975, 3910, 5041, 6388, 8047, 9958, 12262, 14894, 17920, 21346, 25347, 29796, 34875, 40522, 46854, 53826, 61716, 70274, 79883, 90380, 101875, 114346, 127981, 142612, 158737, 176086, 194827, 214852, 236717, 259906, 285124, 311970, 340588, 370990, 403819, 438440, 475556
OFFSET
0,2
COMMENTS
Note that this figure can be obtained by drawing an "equatorial" line through the middle of the strip of n adjacent rectangles in A306302. This cuts each of the 2n "equatorial" cells in A306302 in two. It follows that 2*a(n) = A306302(n) + 2*n, i.e. that a(n) = A306302(n)/2 + n. Note that there is an explicit formula for A306302(n) in terms of n. - Scott R. Shannon, Sep 06 2022.
This means the present sequence is one more member of the large class of sequences which are essentially the same as A115004 (see Cross-References). - N. J. A. Sloane, Sep 06 2022
LINKS
Scott R. Shannon, Image for a(4) = 56. Note in this and other images the entire 2xn array is shown so the number of cells is twice a(n).
Scott R. Shannon, Image for a(6) = 196.
Scott R. Shannon, Image for a(10) = 1138.
Scott R. Shannon, Image for a(15) = 5041.
FORMULA
a(n) = A356790(2,n+2)/2 - 2.
CROSSREFS
The following nine sequences are all essentially the same. The simplest is A115004(n), which we denote by z(n). Then A088658(n) = 4*z(n-1); A114043(n) = 2*z(n-1)+2*n^2-2*n+1; A114146(n) = 2*A114043(n); A115005(n) = z(n-1)+n*(n-1); A141255(n) = 2*z(n-1)+2*n*(n-1); A290131(n) = z(n-1)+(n-1)^2; A306302(n) = z(n)+n^2+2*n; A355902(n) = n + A306302(n)/2. - N. J. A. Sloane, Sep 06 2022
Sequence in context: A343584 A335970 A212967 * A301410 A333897 A316937
KEYWORD
nonn
AUTHOR
STATUS
approved